How to collide fluids to form vortex
You cannot visualize vortex with fluid simulation voxel data, because there is nothing moving inside the fluid mesh, it all happens on the fluid's surface.

You would have to use 2 interacting domains and form the vortex with their interface by mixing them. This cannot be done in Blender since multiple domains cannot interact. You can simulate only 1 domain in scene, although you can playback multiple domains from baked files in single scene.

There are Trace particles for visualizing the movement of voxel liquid. Add some dummy mesh object (plane) into scene, enable fluid and set type to Particle and check Tracer. Under Domain > Fluid Particles set their count. But these particles are not always behaving nice (they stick to walls, play dead).

So you might want to use SPH Fluid Particle simulation instead and get a very nice vortex. If you mesh these particles with the CubeSurface addon you could also color the opposing streams differently so the render will be nice.